Scala analysis: diet
Diatonic-type scale inside Wookie[58]
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 203.509 cents 203.508772 2: 392.982 cents 392.982456 3: 498.246 cents 498.245614 4: 701.754 cents 701.754386 5: 891.228 cents 891.228070 6: 1094.737 cents 1094.736842 7: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 105.2632 cents 105.2632 1: 203.5088 cents 203.5088 2: 189.4737 cents 189.4737 3: 105.2632 cents 105.2632 4: 203.5088 cents 203.5088 5: 189.4737 cents 189.4737 6: 203.5088 cents 203.5088 7: 105.2632 cents 105.2632
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 105.26316 cents 1: 2 189.47368 cents 1: 3 203.50877 cents 2: 1 294.73684 cents 2: 3 308.77193 cents 2: 3 392.98246 cents 3: 5 498.24561 cents 3: 1 512.28070 cents 3: 1 596.49123 cents 4: 1 603.50877 cents 4: 1 687.71930 cents 4: 5 701.75439 cents 5: 3 807.01754 cents 5: 3 891.22807 cents 5: 1 905.26316 cents 6: 3 996.49123 cents 6: 2 1010.52632 cents 6: 2 1094.73684 cents Highest number of different intervals for one interval class: 3 Average number of different intervals per interval class: 3.00000 = 3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 203.5 393.0 498.2 701.8 891.2 1094.7 1200.0 203.5 : 189.5 294.7 498.2 687.7 891.2 996.5 1200.0 393.0 : 105.3 308.8 498.2 701.8 807.0 1010.5 1200.0 498.2 : 203.5 393.0 596.5 701.8 905.3 1094.7 1200.0 701.8 : 189.5 393.0 498.2 701.8 891.2 996.5 1200.0 891.2 : 203.5 308.8 512.3 701.8 807.0 1010.5 1200.0 1094.7: 105.3 308.8 498.2 603.5 807.0 996.5 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 105.2632 .. 203.5088 cents 98.24561 cents 105.26316 cents 2: 294.7368 .. 392.9825 cents 98.24561 cents 91.22807 cents 3: 498.2456 .. 596.4912 cents 98.24561 cents 105.26316 cents 4: 603.5088 .. 701.7544 cents 98.24561 cents 7.01754 cents 5: 807.0175 .. 905.2632 cents 98.24561 cents 105.26316 cents 6: 996.4912 .. 1094.7368 cents 98.24561 cents 91.22807 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 105.26316 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 203.50877 cents Average / Smallest step : 1.628571 Largest / Average step : 1.187135 Largest / Smallest step : 1.933333 Median interval of one step : 189.47368 cents, amount: 2 Most common interval of one step : 203.50877 cents, amount: 3 Least squares average step : 176.54135 cents, oct.: 1235.78947 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 171-tone equal temperament with octave 1200.000 cents degrees: 29 56 71 100 127 156 171 Least number of segments generator : 86 of 603.509 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 149 of 1045.614 cents and inv. generated superset size: 36 = 29 more = 514.286% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCABAC Step pattern size order : LMSLMLS Interval vector is [ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 2 0 3 0 0 0 0 0 0 0 0 0 0 0 0 1 0 3 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 0 1 0 0 0 0 0 0 0 0 0 0 0 1 ] Scale is a Constant Structure, by a margin of 7.01754 cents Scale diversity : 1.346855 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.508772 Rothenberg efficiency : 0.544218 redundancy: 0.455782 Efficiency x scale size : 3.809524 Number of different interval sizes : 18 = 3.00000 / class Number of one step interval sizes : 3 Highest interval variety : 3 Mean interval variety : 3.00000 = 3 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 7.01754 cents Most common intervals : 498.24561 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 392.982 701.754 cents Most common triad is 0.0 498.246 701.754 cents, amount: 3 Number of recognisable fifths : 6, average 699.4152 cents Number of appreciable fifths : 5, average 701.7544 cents Scale is Lydian octave species of abstract tetrachord Best fifths form a closed circle Best major thirds form a closed circle Best minor thirds form a closed circle Formal octave complements present : 3 = 42.8571% Limited inverse transpositions with margin 98.2456 cents: 2 -- Rational properties --
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 37.0249 c. M: 66.1654 c. Lebeng 9: 2 1 1 1 2 1 1 P M ME S SD: 35.9787 c. M:-63.1579 c. 10: 2 1 1 2 1 2 1 P M ME S SD: 29.0977 c. M: 51.2281 c. Sethares Neutral, Beatles-7, Dichotic-7 11: 2 2 1 1 2 2 1 P D3 S SD: 31.4223 c. M:-47.2089 c. 12: 2 2 1 2 2 2 1 P M ME S SD: 4.9622 c. M:-8.7719 c. G.Lydian, M.Ionian, M.Hypolydian, Major, Bilaval That, Mela Shankarabharanam, Raga Atana, Ghana Heptatonic, Peruvian Major, Matzore, Rast ascending: Greece, 4th plagal Byzantine, Ararai: Ethiopia, Makam Cargah, Ajam Ashiran, Dastgah-e Mahur, Dastgah-e Rast Panjgah, Xin: China, DS2, Heptatonia prima 43: 7 7 4 7 7 7 4 SP M DE S SD: 4.6110 c. M: 8.1599 c. Forty-three tone Major 46: 8 7 4 8 7 8 4 P T3 SD: 2.9822 c. M:-5.1869 c. Forty-six tone "Just" Major 58: 10 9 5 10 9 10 5 P T3 SD: 1.8126 c. M:-3.3878 c. 70: 12 11 6 12 11 12 6 P T3 SD: 1.4552 c. M:-2.4060 c. 82: 14 13 7 14 13 14 7 P T3 SD: 1.5803 c. M:-2.8241 c. 89: 15 14 8 15 14 15 8 SP T3 SD: 1.4560 c. M: 2.6020 c. 101: 17 16 9 17 16 17 9 SP T3 SD: 1.0086 c. M: 1.6675 c. 113: 19 18 10 19 18 19 10 SP T3 SD: 0.9303 c. M: 1.7389 c. 147: 25 23 13 25 23 25 13 SP T3 SD: 0.8101 c. M: 1.4322 c. 159: 27 25 14 27 25 27 14 SP T3 SD: 0.3745 c. M: 0.6620 c. 171: 29 27 15 29 27 29 15 SP T3 SD: 0.0000 c. M:-0.0000 c.
FIT/HARMONIC
1 x x x x x x 2 S SD: 0.0000 cents 2 x x x 3 x x 4 S SD: 0.1003 cents 3 x x 4 x 5 x 6 S SD: 2.2908 cents 4 x 5 x 6:7 x 8 S SD: 19.4710 cents 5 x 6:7 x 8:9:10 S SD: 31.6518 cents 6:7 x 8:9:10:11:12 S SD: 13.0393 cents 7:8:9 x 11:12:13:14 SD: 17.7504 cents 8:9:10:11:12:13:15:16 SD: 10.5692 cents 10:11 x 13:15:17:19:20 SD: 11.1105 cents 12:14:15:16:18:20:23:24 SD: 10.2060 cents 14:16:18:19:21:23:26:28 SD: 10.1068 cents 15:17:19:20:23:25:28:30 SD: 6.6233 cents 16:18:20:21:24:27:30:32 S SD: 4.6402 cents 24:27:30:32:36:40:45:48 S SD: 1.6521 cents 58:65:73:77:87:97:109:116 SD: 1.6438 cents 66:74:83:88:99:110:124:132 SD: 1.4290 cents 74:83:93:99:111:124:139:148 SD: 1.2723 cents 82:92:103:109:123:137:154:164 SD: 1.2129 cents 86:97:108:115:129:144:162:172 SD: 1.0370 cents 98:110:123:131:147:164:184:196 SD: 0.9828 cents 102:115:128:136:153:171:192:204 SD: 0.7607 cents 114:128:143:152:171:191:215:228 SD: 0.7475 cents 126:142:158:168:189:211:237:252 SD: 0.5748 cents 138:155:173:184:207:231:260:276 SD: 0.5043 cents 144:162:181:192:216:241:271:288 SD: 0.4261 cents 168:189:211:224:252:281:316:336 SD: 0.2896 cents 264:297:331:352:396:442:497:528 SD: 0.2678 cents 282:317:354:376:423:472:531:564 SD: 0.2253 cents 306:344:384:408:459:512:576:612 SD: 0.1377 cents 408:459:512:544:612:683:768:816 SD: 0.1365 cents 432:486:542:576:648:723:813:864 SD: 0.0933 cents 600:675:753:800:900:1004:1129:1200 SD: 0.0911 cents